, Limits
·
state and work with definition of limit
·
Demonstrate , describe and recognize ways
in which limits do not exist
· calculate derivatives of functions (10 calc)
· Write and explain the definition of absoulte
masc and min of a function .
Def : the behaviour of a function as the
independent variable a certain
approaches value .
Lo
f(x) = x + 1 as "x"approaches "1"
x
1. &
,
1 80
.
,
1 .
594/1/ 1 000
,
,
1 , 001
,Note
:
·
Lim-fas : meany Limit a -c from left
himt fas ! limit + right
·
means from
· Lim - f(x)
, " means limit a -
from both
if n and k are constant then :
① Limock = k
② Limocx = C
O
3 Limo-cx = ch ④ Limoc 1fca) =
n time fa)
O
S Limo (fog(s]
=
Limayfe Lima (g(x)
2 .
98
a) Lim + 26 = or
b Lim +23x2 = 312 = 122
c)
Limx
3x + 4 =
3(1) + 4
= 0 . 88h
+
15x + 7
3(1) +7
↓) Lima1-Ecs where ~x-252, if <
2x else
( -
2)2 =
1
, # Limits in the form of (8)
can be found by either :
① dividing certain factors and
out
getting rid ofdenomi
② ration lize the numerator or denominator
③ use formula L'hospitals rule :
f (x)
Ling =
Linc , y x
2 .
g8
2 4
x
-
6) Lim z x -
2
(x -
2)(x + 2)
(x -
2)
-
x +2
=
4
x2 -
&
b) Lim
* -3 x2 +
35
(x
-
3)(x+ 3)
x(x + 3)
3 3
x 3
-
-
-
=
x -
3
= 2
·
state and work with definition of limit
·
Demonstrate , describe and recognize ways
in which limits do not exist
· calculate derivatives of functions (10 calc)
· Write and explain the definition of absoulte
masc and min of a function .
Def : the behaviour of a function as the
independent variable a certain
approaches value .
Lo
f(x) = x + 1 as "x"approaches "1"
x
1. &
,
1 80
.
,
1 .
594/1/ 1 000
,
,
1 , 001
,Note
:
·
Lim-fas : meany Limit a -c from left
himt fas ! limit + right
·
means from
· Lim - f(x)
, " means limit a -
from both
if n and k are constant then :
① Limock = k
② Limocx = C
O
3 Limo-cx = ch ④ Limoc 1fca) =
n time fa)
O
S Limo (fog(s]
=
Limayfe Lima (g(x)
2 .
98
a) Lim + 26 = or
b Lim +23x2 = 312 = 122
c)
Limx
3x + 4 =
3(1) + 4
= 0 . 88h
+
15x + 7
3(1) +7
↓) Lima1-Ecs where ~x-252, if <
2x else
( -
2)2 =
1
, # Limits in the form of (8)
can be found by either :
① dividing certain factors and
out
getting rid ofdenomi
② ration lize the numerator or denominator
③ use formula L'hospitals rule :
f (x)
Ling =
Linc , y x
2 .
g8
2 4
x
-
6) Lim z x -
2
(x -
2)(x + 2)
(x -
2)
-
x +2
=
4
x2 -
&
b) Lim
* -3 x2 +
35
(x
-
3)(x+ 3)
x(x + 3)
3 3
x 3
-
-
-
=
x -
3
= 2
